A167519 Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.

3, 10, 11, 12, 11000, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119, 11121, 11122, 11123, 11124, 11125, 11126, 11127, 11128, 11129, 11131, 11132, 11133, 11134, 11135, 11136, 11137, 11138, 11139, 11141, 11142, 11143, 11144

Offset: 1

Author

M. F. Hasler, Nov 05 2009

Keywords

• nonn
• base

Comments

The terms of the sequence give the positions of the digits '0' in the string formed by concatenating all the terms (written in base 10).

Examples

			The sequence cannot start with 1 (which would mean it starts with 0) or 2 (which would mean that the second term equals 0), so a(1)=3 is the smallest possibility.
Thereafter, the smallest possible value for a(2), which must have '0' as second digit, is a(2)=10.
This means that the next digit '0' must occur at position 10; up to there, we use the smallest possible values for a(3)=11 and a(4)=12.
Then must follow two nonzero digits (which must be part of a(5)) and then three zero digits (from a(2),a(3),a(4) = 10, 11, 12). None of the latter can be the first digit of a(6), so they must be part of a(5), for which the smallest possibility is therefore a(5)=11000.
This also means that there is no digit '0' between the 12th digit (= the last digit of a(6)), and the 11000th digit of the sequence. So there follow roughly 11000/5 terms which are the smallest possible 5-digit terms without a zero digit.
		

Crossrefs

Cf. A167500-A167503. See A210414 for another version.

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

Definition corrected by Jaroslav Krizek, Jun 19 2014